Theo Verelst Switched Filter page

By using a pulse width ratio as a VCF control, a switched variable
filter design yields a straighforward circuit, with large range
cutoff frequency control. Variations and simulation results
are and wil appear on this page.

First order idealized switched filter

The simplest switched frequency controlled filter is depicted
below.

The input frequency is sweeped, the filter
cutoff frequency is determined by the switch on time (50 percent
in this case) and the resistor networks effecitve value,
roughly 16 kOhm, and is roughly 1kHz here (quick computation
seems to match graphical results, wil do more acurate analysis).
The sampling frequency is 100kHz, which makes
for easy anti-aliasing filtering, and when the
filter clock is linked with a sample generator clock, there is
no need for an input anti aliasing filter.

A forth order version

A forth order version is produced by cascading 4 buffered 1st
order versions.
I'll immedeately continue to the version with a feedback or
'resonance' loop:

The digital pule is 100kHz with 80 percent duty cycle, the input
signal is a frequency sweeped sine wave.

Adding a feedback for 'resonance' control

By setting the feedback control to -3.9, a near oscilating
system is obtained. The results in
time-amplitude form are:

The sweeped sine can be seen in the the blowup of the peak,
and it is clear that after the filter has been exitated, the
resonating filter component in the output (a damped oscilation)
takes quite some time to damp out, and interferes with the input
signal.

This can also be seen in the frequency analysis:

Two parts are easily distinguished (I'd include more views
if I had the web space): the sweeped oscilator , which is
heavily damped at the ends of the frequency axis, and the
damped oscilation, which remains equal in frequency.

Note that the sample time is almost half a second, and
that the sample frequency is 100kHz, which led to hours of
simulation time, but I guess there is room for improving this.

(Also in switched version, i.e. switch based amplitude feed?)

Finally of course: what does it
sound
like? This is a downsampled version, for easier listening
(the original is 400mS long).

Sampling noise (distortion) and proposed improvements

Make spike or integrated (averaged) input samples possibly per stage.

Non-ideal, actual parts

Library limited to 4016 switches (would prefer 4066 or 74HC equiv.).

Adding non-linearities

For synthesizer use, a multi pole filter can have distortions
in various phases or its signal path to beef the sound up, and
to become more characteristic. Diode - resistor networks can do
the trick, transistors too, and I migh even try a DA steered
non-linearity.